A Base Point Free Theorem of Reid Type

Abstract

Assume that $X$ is a normal projective variety over ${\Bbb C}$, of dimension $\leqq 3$, and that $(X, Δ)$ is a log variety that is weakly Kawamata log terminal. Let $L$ be a nef Cartier divisor such that $aL-(K_X+Δ)$ is nef and log big on $(X, Δ)$ for some $a\in{\Bbb N}$. Then Bs$|mL|=\emptyset$ for every $m\gg 0$.